Very high resolution spectra of high Rydberg states of the argon atom with principal quantum numbers in the range n = 60-200 have been measured in double-resonance experiments using a high resolution vacuum ultraviolet laser and frequency stabilized, millimeter waves. The 250 kHz resolution achieved in the double-resonance spectra enables the determination of accurate effective quantum numbers and the precise measurement of fine-structure intervals in l = 0-3 Rydberg states at n values much beyond 50. The high resolution is also used to detect spectral shifts induced by small electric fields. Analysis of these spectral shifts allows the determination of stray electric fields with uncertainties of less than 1 mV/cm and their compensation to less than 1 mV/cm. The spectra of high Rydberg states are very strongly influenced by experimental conditions and the highest resolution can only be obtained when the stray electric fields are reduced to less than l mV/cm and the intensity of the millimeter waves are reduced to much less than 1 mu W/cm(2). High resolution measurements on the very high Rydberg states probed by pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectroscopy are also reported. These spectra are strongly influenced by the inhomogeneous electric field of ions and other Rydberg states located in the photoexcitation region. These fields induce a strong mixing of the optically accessible low-l Rydberg states with nonpenetrating high-l Rydberg states. These results conclusively demonstrate the important role played by ions in PFI-ZEKE spectroscopy.